If you establish that π is the ratio of a circle's circumference to its diameter, you can approximate the value of π using the "method of exhaustion" by inscribing a polygon inside the circle of radius r and then circumscribing a larger polygon outside the same circle.

The circumference of the circle (c) will lie somewhere between the perimeter of the smaller polygon (p₁) and the perimeter of the larger polygon (p₂). Therefore the value of π is somewhere between p₁/2r and p₂/2r.

As the polygon becomes many-sided, the estimate gets more and more accurate.